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    An optimal PID controller design for nonlinear constrained optimal control problems

    Access Status
    Open access via publisher
    Authors
    Li, B.
    Teo, Kok Lay
    Lim, C.
    Duan, G.
    Date
    2011
    Type
    Journal Article
    
    Metadata
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    Citation
    Li, Bin and Teo, Kok Lay and Lim, Cheng Chew and Duan, Guang Ren. 2011. An optimal PID controller design for nonlinear constrained optimal control problems. Discrete and Continuous Dynamical Systems B. 16 (4): pp. 1101-1117.
    Source Title
    Discrete and Continuous Dynamical Systems B
    DOI
    10.3934/dcdsb.2011.16.1101
    ISSN
    15313492
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/34867
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we consider a class of optimal PID control problems subject to continuous inequality constraints and terminal equality constraint. By applying the constraint transcription method and a local smoothing technique to these continuous inequality constraint functions, we construct the corresponding smooth approximate functions. We use the concept of the penalty function to append these smooth approximate functions to the cost function, forming a new cost function. Then, the constrained optimal PID control problem is approximated by a sequence of optimal parameter selection problems subject to only terminal equality constraint. Each of these optimal parameter selection problems can be viewed and hence solved as a nonlinear optimization problem. The gradient formulas of the new appended cost function and the terminal equality constraint function are derived, and a reliable computation algorithm is given. The method proposed is used to solve a ship steering control problem.

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